> First off correlation != causation.
These are more powerful than the usual designs. For example, the correlation of intelligence with longevity survives a within-family sibling study which controls away all effects of family SES and shared environment https://academic.oup.com/ije/article/doi/10.1093/ije/dyx168/... You can also verify this using twin comparisons eg http://ije.oxfordjournals.org/content/early/2015/07/24/ije.d... .
More importantly, because so much of the underlying genetics of intelligence has been found and are covered by the GWAS's polygenic scores, it is possible to compare with the genetics for scores or hundreds of other diseases and measures of health: https://en.wikipedia.org/wiki/Genetic_correlation#Intelligen... https://en.wikipedia.org/wiki/Genetic_correlation#Education The correlation is invariably negative: higher genetic potential for intelligence predicts lower disease and better health.
> If we need to edit multiple genes, genes that are also tied to other traits, that's what's driving the chance of side effect, not the increased intelligence.
Whether it is horizontal or vertical pleiotropy is irrelevant; it is irrelevant whether a particular SNP decreases risk of heart disease by increasing one's level of education so one knows to exercise regularly, or if it instead avoids a bad mutation which makes mitochondria slightly more inefficient thereby damaging the brain & heart. You want that SNP regardless of which causal pathway it is. If intelligence polygenic scores predict lower risk for disease and better health, then doing embryo selection or editing based on that will in fact do what it's supposed to.